Question

A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance R₁ in series with the coil. If a resistance R₂ is connected in series with it, then it can measures upto V/2 volts. Find the resistance, in terms of R₁ and R₂, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R₁ and R₂

Answer 1

A high resistance that is connected in series with the galvanometer to convert it into voltmeter. The value of the resistance is given by `R=V/I_g-G`

Here,
V = Potential difference across the terminals of the voltmeter

I_g = Current through the galvanometer

G = Resistance of the galvanometer

When resistance R₁ is connected in series with the galvanometer,

`R_1=V/I_g-G`

When resistance R₂ is connected in series with the galvanometer,

 `R_2=V/(2I_g)-G" .....(ii)"`

From (i) and (i), we get

`V/(2I_g)=R_1-R_2 " and "G=R_1-2R_2`

The resistance R₃ required to convert the given galvanometer into voltmeter of range 0 to 2V is given by

`R_3=(2V)/I_g-G`

⇒R₃=4(R₁−R₂)−(2R₁−R₂)=3R₁−2R₂

G in terms of R₁ and R₂ is given by

G=R₁−2R₂